Optimal Parameter Extraction of PEM Fuel Cell Using a Hybrid Weighted Mean of Vectors and Nelder-Mead Simplex Method

Abstract

Accurate modeling is an important aspect for a reliable design, control and optimization of proton exchange membrane (PEM) fuel cell. The mathematical model of PEM fuel cell involves a set of non-linear equations and is considered as multi-variate, multi-modal and non-linear optimization problem having seven unidentified parameters. This paper proposes a new hybrid approach based on weIghted meaN oF vectOrs and Nelder-Mead (INFONM) method for PEM fuel cell parameter extraction. An optimization problem is framed and a sum of squared error (SSE) based objective function is formulated between estimated and experimental voltages. The effectiveness of the developed approach is evaluated on four available benchmark fuel cell data sheets such as NedStack PS6, BCS 500 W, 250 W and Ballard Mark V fuel cell stacks. A fair comparison is presented with well-established algorithms as well as existing literature work to demonstrate the superiority of INFONM. The results reveal that hybrid approach produces better outcomes in terms of accuracy, reliability and effectiveness as compared to other algorithms. Also, the good closeness between the estimated and experimental polarization curves proves that hybrid approach accurately determines unknown parameters. The obtained value of SSE for NedStack PS6, BCS 500 W, 250 W and Ballard Mark V PEM fuel cell stacks are 1.242, 0.0111, 0.317, and 0.619 respectively whereas, the maximum values of percentage voltage deviations are −1.076%, 0.458%, 1.688%, and 2.69% respectively. Furthermore, statistical indices such as mean, minimum, standard deviation, and maximum value of SSE for hybrid approach indicate a least value among all other algorithms which elucidates hybrid approach as more robust and efficient. Additionally, the convergence curves, box plot study and non-parametric test further validate the robustness and reliability of INFONM in identifying unknown parameters of PEM fuel cell. Moreover, a sensitivity analysis considering SOBOL indicators is also presented to provide an illustration of influence of variation in extracted parameters on PEM fuel cell model.

Keywords

• PEM fuel cell
• parameter extraction
• polarization characteristics
• Nelder-Mead
• weighted mean of vector optimization
• statistical analysis